Isobaric Vapor−Liquid Equilibria for Binary and Ternary Systems

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J. Chem. Eng. Data 2000, 45, 564-569

Isobaric Vapor-Liquid Equilibria for Binary and Ternary Systems Composed of 2-Methoxy-2-methylpropane, Ethanol, 2-Methyl-2-propanol, and Octane at 101.3 kPa Toshihiko Hiaki* and Kazuteru Tatsuhana Department of Industrial Chemistry, College of Industrial Technology, Nihon University, 1-2-1, Izumi-cho, Narashino, Chiba 275-8575, Japan

Isobaric vapor-liquid equilibria for two ternary systems, 2-methoxy-2-methylpropane (MTBE) + ethanol + 2-methyl-2-propanol and ethanol + 2-methyl-2-propanol + octane, and one binary system, ethanol + 2-methyl-2-propanol, have been measured at 101.3 kPa. The measurements were made in an equilibrium still with circulation of both the vapor and liquid phases. Both ternary systems and the binary system ethanol + 2-methyl-2-propanol do not form azeotropes. The three constituent binary systems of MTBE + ethanol, MTBE + 2-methyl-2-propanol, and 2-methyl-2-propanol + octane, which were measured in our previous work, are also not azeotropes. The other constituent system ethanol + octane, measured in our previous work, forms a minimum azeotrope. The experimental data for the binary systems were correlated with the nonrandom two-liquid (NRTL) equation. The NRTL equation yielded a good prediction of activity coefficients for the ternary systems from the parameters of the correlated binary systems.

Introduction

Table 1. Normal Boiling Points, Tb, and Refractive Index, nD, of the Components

Ethers and alcohols used as gasoline additives have excellent antiknock qualities and are considered environmental protection substances. Gasoline including 2-methoxy-2-methylpropane (MTBE) has been used for a highperformance premium gasoline. In recent years, mixtures of ethers with alcohols have been considered for blending with gasoline. As a continuation of our studies1,2 on the vapor-liquid equilibrium (VLE) of MTBE + octane + alcohols systems, the isobaric VLE for the ternary systems MTBE + ethanol + 2-methyl-2-propanol and ethanol + 2-methyl-2-propanol + octane and the constituent binary system ethanol + 2-methyl-2-propanol have been measured at 101.3 kPa. The measurements were made in an equilibrium still3 with circulation of both the vapor and liquid phases. Data for the other four constituent binary systems of MTBE + ethanol,1 MTBE + 2-methyl-2-propanol,2 2-methyl-2-propanol + octane,2 and ethanol + octane4 were reported in our previous studies. For the ethanol + 2-methyl-2-propanol system, one set of isobaric VLE data at 101.3 kPa is reported by Suska et al.5 and one set of isothermal data at 313.15 K have been measured by Oracz.6 No isobaric or isothermal VLE data have been reported previously for the MTBE + ethanol + 2-methyl-2-propanol and ethanol + 2-methyl-2-propanol + octane systems. Experimental Section Materials. Ethanol, 2-methyl-2-propanol, and octane, supplied by the Wako Pure Chemical Co. Ltd., and MTBE, supplied by the MercksDr. Th. Schuchardt & Co., were special grade reagents. Ethanol was used after a small quantity of water was removed with 3A molecular sieves. Gas-chromatographic analysis on all three materials indicated that each had a purity of at least 99.9 mol %. The measured physical properties of the compounds are listed * Corresponding author. E-mail address: [email protected].

Tb/K

nD(298.15 K)

material

exptl

calca

lit.

exptl

lit.

MTBE ethanol 2-methyl-2propanol octane

328.14 351.44 355.53

328.36 351.45 355.49

328.11b 351.443c 355.50c

1.366 41 1.359 37 1.384 90

1.3663b 1.35941c 1.39389c

398.80

398.82

398.823c

1.395 15

1.39565c

b

a Calculated value using the Antoine constants with Table 2. Arce et al.11 c Riddick et al.12

in Table 1 along with the literature data. Refractive index values were determined with a digital refractometer by using the critical angle of total reflection method (Kyoto Electric RA-510, Japan). Refractive index was measured with an accuracy of (0.00005. Procedure. An all Pyrex-glass equilibrium still with circulation of vapor and liquid phases, developed in a previous study,3 was used for the determination of VLE values. The overall charge of the apparatus was about 100 cm3 of solution. The temperature was measured with a calibrated platinum resistance thermometer (Pt 100Ω) with an accuracy of 0.03 K. A standard resistance thermometer (Chino Co. model R800-2, Japan), calibrated on the ITS-90 scale, was used for this calibration. The pressure in the apparatus was measured by means of a silicon resonant precision barometer (Tokyo Suzuki Seisakusho Co., model T60, Japan) with an accuracy of 0.015 kPa. Since the barometric pressure changed slightly, the experimental temperatures were corrected to 101.3 kPa.1 Analysis. The equilibrium composition of the samples was determined by using a gas chromatograph (GL Sciences model GC-380, Japan) equipped with a flame ionization detector and an autosampler. The column packing was Gasukuropack 54 (supplied by the GL Sciences Inc.). The

10.1021/je990287j CCC: $19.00 © 2000 American Chemical Society Published on Web 06/02/2000

Journal of Chemical and Engineering Data, Vol. 45, No. 4, 2000 565 Table 2. Antoine Constants of the Componentsa material

A

B

C

ref

MTBE ethanol 2-methyl-2-propanol octane

6.120 19 7.242 22 6.352 72 6.043 94

1190.420 1595.811 1105.198 1351.938

-39.040 -46.702 -101.256 -64.030

b c c c

a log(P/kPa) ) A - B/[(T/K) + C]. e Tsuji et al.13 al.14

f

Boublik et

Table 3. Isobaric Vapor-Liquid Equilibrium Data, Temperature, T, Liquid Phase, x1, and Vapor Phase, y1, Mole Fractions, and Activity Coefficient, γi, for the Ethanol (1) + 2-Methyl-2-propanol (2) System at 101.3 kPa T/K

x1

y1

γ1

γ2

355.53 355.43 355.35 355.29 355.24 355.12 354.95 354.78 354.70 354.49 354.41 354.26 354.02 353.87 353.76 353.67 353.43 353.35 353.22 352.97 352.58 352.48 352.26 352.18 352.06 351.94 351.91 351.87 351.71 351.44

0.0000 0.0343 0.0721 0.0978 0.1175 0.1727 0.2402 0.3020 0.3341 0.3996 0.4236 0.4650 0.5284 0.5636 0.5904 0.6110 0.6618 0.6776 0.7033 0.7524 0.8224 0.8408 0.8780 0.8919 0.9121 0.9303 0.9347 0.9417 0.9659 1.0000

0.0000 0.0371 0.0779 0.1056 0.1269 0.1861 0.2586 0.3249 0.3595 0.4296 0.4556 0.4993 0.5661 0.6027 0.6306 0.6510 0.7017 0.7182 0.7430 0.7902 0.8544 0.8706 0.9023 0.9140 0.9309 0.9457 0.9492 0.9549 0.9739 1.0000

0.9257 0.9273 0.9293 0.9314 0.9333 0.9390 0.9443 0.9477 0.9546 0.9576 0.9616 0.9686 0.9724 0.9755 0.9766 0.9808 0.9835 0.9853 0.9892 0.9936 0.9943 0.9952 0.9957 0.9965 0.9969 0.9971 0.9973 0.9977

0.9998 0.9997 0.9997 0.9993 0.9986 0.9973 0.9951 0.9928 0.9889 0.9861 0.9828 0.9757 0.9710 0.9663 0.9646 0.9579 0.9519 0.9483 0.9373 0.9209 0.9169 0.9115 0.9084 0.9020 0.8978 0.8969 0.8944 0.8915

relationship between peak area and composition was determined from analysis of samples of known composition. The accuracies of liquid, xi, and vapor, yi, mole fractions are estimated to be 0.002 mole fraction. Experimental Results The activity coefficients γi were calculated with the equation

Pyi ) γiPiSxi

(1)

In most cases it is preferable to calculate the activity coefficients by including fugacity coefficients and the Poynting factor correction. However, not all the required physical property data are available for MTBE to calculate these terms accurately. The activity coefficients were therefore calculated on the assumption of an ideal vapor phase. The vapor pressures of the pure components, PiS, were obtained using the Antoine equation constants, which are shown in Table 2. Binary System. The binary VLE data for ethanol (1) + 2-methyl-2-propanol (2) are reported in Table 3 along with the activity coefficients calculated using eq 1. The values of ln γi are negative for the whole concentration range. The ethanol + 2-methyl-2-propanol system is nonazeotropic.

Figure 1. Temperature-composition diagram for ethanol (1) + 2-methyl-2-propanol (2) at 101.3 kPa. Present work: O, x1; b, y1. Suska et al.5 at 101.3 kPa (1970): 4, x1; 2, y1. s, NRTL equation with parameters from Table 6.

Figure 2. Activity coefficient-liquid composition diagram for ethanol (1) + 2-methyl-2-propanol (2) at 101.3 kPa. Present work: O, ln γ1; b, ln γ 2. Suska et al.5 at 101.3 kPa (1970): 4, ln γ1; 2, ln γ 2. s, NRTL equation with parameters from Table 6.

The experimental VLE for the ethanol (1) + 2-methyl-2propanol (2) system is shown graphically in Figures 1 and 2. The three constituent binary systems of MTBE + ethanol, MTBE + 2-methyl-2-propanol, and 2-methyl-2-propanol + octane, which were measured in our previous work, are nonazeotropes. As seen in our previous work, the other constituent system, ethanol + octane, forms a minimum boiling azeotrope. The experimental data were tested for thermodynamic consistency using the point test of Fredenslund et al.7 and of Van Ness et al.8 The area test is not employed in this case because this system is almost ideal. The results indicate that the experimental data for the binary system of ethanol + 2-methyl-2-propanol are thermodynamically consistent. Ternary System. The experimental VLE data for the ternary system MTBE (1) + ethanol (2) + 2-methyl-2propanol (3) at 101.3 kPa are reported in Table 4. The tie lines and isotherms based on the experimental data for the

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Journal of Chemical and Engineering Data, Vol. 45, No. 4, 2000

Table 4. Isobaric Vapor-Liquid Equilibrium Data, Temperature, T, Liquid Phase, xi, and Vapor Phase, yi, Mole Fractions, and Activity Coefficient, γi, for MTBE (1) + Ethanol (2) + 2-Methyl-2-propanol (3) at 101.3 kPa T/K

x1

x2

y1

y2

γ1

γ2

γ3

T/K

x1

x2

y1

y2

γ1

γ2

γ3

350.54 349.85 350.64 349.11 350.00 349.26 351.04 348.13 350.32 349.69 350.92 348.96 347.21 349.54 348.96 346.32 351.01 347.97 350.29 350.91 350.43 346.91 349.51 346.34 348.16 346.14 349.74 350.30 345.15 344.95 346.04 346.75 343.85 349.70 343.59 344.82 345.54 348.31 347.31 342.82 348.40 343.56 346.24 345.22 347.43 346.06 345.12 347.49 346.50 344.96 344.89 342.45 346.48 343.66 342.84 341.79 343.92 341.01 343.94 340.39 344.67 341.33 343.92 342.47 339.49 340.84 342.55 342.54 340.99 338.99 344.60 339.96 343.63 339.40

0.024 0.026 0.028 0.030 0.031 0.034 0.052 0.058 0.059 0.063 0.064 0.065 0.066 0.067 0.070 0.071 0.072 0.073 0.073 0.081 0.081 0.082 0.083 0.087 0.091 0.092 0.092 0.095 0.096 0.101 0.105 0.106 0.107 0.108 0.113 0.117 0.120 0.123 0.125 0.126 0.130 0.130 0.132 0.134 0.140 0.144 0.147 0.148 0.156 0.160 0.161 0.163 0.168 0.171 0.173 0.175 0.180 0.182 0.187 0.193 0.195 0.195 0.196 0.197 0.200 0.201 0.203 0.206 0.212 0.213 0.215 0.216 0.217 0.222

0.802 0.866 0.735 0.933 0.790 0.858 0.373 0.733 0.414 0.484 0.257 0.560 0.789 0.458 0.520 0.844 0.146 0.614 0.284 0.078 0.161 0.669 0.314 0.703 0.553 0.694 0.177 0.087 0.763 0.753 0.584 0.487 0.826 0.096 0.818 0.635 0.533 0.147 0.269 0.806 0.082 0.689 0.361 0.584 0.161 0.303 0.395 0.092 0.179 0.328 0.337 0.603 0.104 0.425 0.494 0.605 0.353 0.653 0.320 0.655 0.166 0.541 0.417 0.456 0.712 0.573 0.389 0.356 0.502 0.707 0.081 0.587 0.181 0.622

0.098 0.111 0.112 0.123 0.125 0.137 0.172 0.218 0.197 0.211 0.198 0.223 0.238 0.221 0.236 0.257 0.213 0.251 0.223 0.224 0.238 0.279 0.252 0.292 0.262 0.302 0.265 0.251 0.321 0.330 0.336 0.328 0.350 0.278 0.361 0.368 0.363 0.332 0.352 0.386 0.337 0.394 0.371 0.396 0.365 0.392 0.404 0.375 0.398 0.425 0.425 0.445 0.411 0.451 0.463 0.470 0.456 0.477 0.460 0.497 0.467 0.497 0.439 0.482 0.506 0.503 0.492 0.498 0.516 0.521 0.486 0.521 0.498 0.530

0.772 0.814 0.708 0.852 0.745 0.788 0.356 0.641 0.388 0.445 0.243 0.505 0.670 0.419 0.466 0.693 0.138 0.535 0.262 0.073 0.149 0.562 0.283 0.578 0.485 0.567 0.161 0.081 0.599 0.588 0.471 0.404 0.615 0.087 0.604 0.490 0.424 0.127 0.226 0.580 0.071 0.510 0.294 0.443 0.136 0.245 0.311 0.078 0.147 0.256 0.263 0.432 0.085 0.317 0.358 0.420 0.268 0.444 0.244 0.433 0.129 0.372 0.324 0.330 0.456 0.388 0.283 0.259 0.342 0.445 0.063 0.388 0.138 0.401

2.0951 2.1712 2.0460 2.2030 2.0660 2.1374 1.6668 2.0346 1.7098 1.7418 1.5524 1.8425 2.0340 1.7364 1.8024 2.0830 1.4826 1.8936 1.5678 1.3862 1.4915 1.9313 1.6011 1.9387 1.5779 1.9026 1.4980 1.3542 1.9842 1.9509 1.8599 1.7512 2.0190 1.3411 1.9939 1.8853 1.7764 1.4636 1.5667 1.9501 1.4031 1.8851 1.6248 1.7587 1.4508 1.5738 1.6292 1.4072 1.4635 1.5838 1.5819 1.7647 1.4016 1.6359 1.6988 1.7653 1.5646 1.7670 1.5126 1.7619 1.4472 1.6925 1.3846 1.5726 1.7816 1.6935 1.5557 1.5529 1.6384 1.7515 1.3652 1.6782 1.4280 1.6894

0.9982 1.0006 0.9959 1.0025 0.9990 1.0018 0.9695 0.9993 0.9792 0.9867 0.9638 0.9943 1.0070 0.9864 0.9896 1.0086 0.9647 1.0006 0.9671 0.9592 0.9619 1.0075 0.9740 1.0096 1.0011 1.0117 0.9745 0.9720 1.0125 1.0143 1.0024 1.0031 1.0139 0.9699 1.0153 1.0101 1.0088 0.9769 0.9911 1.0223 0.9703 1.0191 1.0024 0.9746 0.9913 1.0044 1.0171 0.9959 1.0037 1.0143 1.0180 1.0346 0.9965 1.0222 1.0271 1.0317 1.0308 1.0422 1.0368 1.0417 1.0243 1.0395 1.0544 1.0429 1.0473 1.0463 1.0451 1.0461 1.0471 1.0521 1.0177 1.0587 1.0491 1.0576

0.9080 0.8871 0.9186 0.8618 0.9054 0.8875 0.9811 0.9070 0.9705 0.9583 0.9900 0.9436 0.8820 0.9640 0.9456 0.8623 0.9930 0.9278 0.9865 1.0048 0.9926 0.9043 0.9802 0.8947 0.9527 0.8971 0.9900 1.0068 0.8711 0.8720 0.9116 0.9407 0.8421 1.0079 0.8402 0.8855 0.9260 0.9918 0.9732 0.8501 1.0027 0.8742 0.9643 0.8696 0.9907 0.9662 0.9546 0.9968 0.9863 0.9609 0.9607 0.8969 1.0004 0.9365 0.9137 0.8785 0.9522 0.8729 0.9663 0.8601 0.9857 0.9015 0.9847 0.9326 0.8436 0.8900 0.9441 0.9473 0.9085 0.8432 1.0036 0.8842 0.9850 0.8688

340.01 342.46 337.80 343.37 341.21 340.16 338.52 340.78 341.67 342.11 337.15 338.65 342.08 337.90 339.32 340.24 337.09 337.64 340.71 336.34 338.14 338.64 338.71 339.12 339.49 334.73 339.17 335.86 336.56 336.00 337.52 337.53 334.34 337.97 336.06 336.10 334.77 334.40 335.89 335.77 336.37 336.56 333.90 334.24 334.35 332.79 332.75 334.06 333.92 334.45 335.08 332.47 332.59 331.71 334.55 332.43 332.79 332.90 333.58 332.98 333.24 333.00 331.57 330.63 331.06 331.42 331.25 330.43 331.19 329.95 330.62 329.35 329.71 328.74

0.234 0.242 0.246 0.247 0.247 0.251 0.253 0.266 0.273 0.274 0.282 0.282 0.284 0.294 0.294 0.308 0.315 0.323 0.327 0.329 0.334 0.335 0.347 0.355 0.357 0.365 0.369 0.372 0.375 0.381 0.399 0.403 0.403 0.406 0.409 0.417 0.425 0.426 0.453 0.461 0.462 0.464 0.466 0.467 0.474 0.476 0.507 0.513 0.514 0.518 0.521 0.528 0.534 0.544 0.551 0.575 0.585 0.588 0.591 0.595 0.609 0.615 0.647 0.650 0.662 0.669 0.700 0.703 0.709 0.747 0.773 0.809 0.825 0.882

0.516 0.201 0.679 0.091 0.384 0.392 0.567 0.284 0.155 0.102 0.607 0.429 0.067 0.460 0.315 0.172 0.470 0.390 0.075 0.501 0.290 0.347 0.192 0.130 0.084 0.549 0.084 0.427 0.320 0.359 0.162 0.147 0.471 0.095 0.270 0.247 0.357 0.394 0.181 0.167 0.107 0.082 0.337 0.301 0.276 0.433 0.358 0.206 0.222 0.157 0.091 0.335 0.309 0.381 0.091 0.242 0.177 0.161 0.101 0.138 0.089 0.103 0.176 0.270 0.198 0.154 0.117 0.189 0.104 0.162 0.064 0.116 0.069 0.073

0.539 0.531 0.555 0.526 0.532 0.560 0.568 0.568 0.568 0.564 0.591 0.593 0.571 0.606 0.600 0.606 0.620 0.627 0.613 0.637 0.637 0.641 0.646 0.647 0.647 0.661 0.658 0.660 0.667 0.674 0.685 0.687 0.682 0.688 0.690 0.697 0.702 0.702 0.718 0.722 0.725 0.727 0.724 0.725 0.729 0.720 0.741 0.752 0.748 0.760 0.762 0.752 0.755 0.770 0.774 0.772 0.789 0.790 0.792 0.799 0.806 0.806 0.812 0.798 0.816 0.821 0.839 0.829 0.845 0.845 0.876 0.878 0.895 0.922

0.343 0.149 0.415 0.069 0.272 0.264 0.355 0.199 0.114 0.075 0.365 0.276 0.049 0.289 0.209 0.121 0.290 0.247 0.054 0.297 0.190 0.220 0.130 0.091 0.059 0.309 0.059 0.260 0.202 0.220 0.108 0.099 0.272 0.065 0.172 0.159 0.214 0.229 0.119 0.111 0.072 0.056 0.201 0.184 0.172 0.249 0.212 0.133 0.143 0.103 0.062 0.199 0.187 0.207 0.063 0.155 0.115 0.107 0.071 0.092 0.062 0.071 0.118 0.173 0.131 0.106 0.084 0.129 0.075 0.119 0.051 0.090 0.057 0.059

1.5994 1.4161 1.6726 1.3348 1.4402 1.5388 1.6287 1.4486 1.3708 1.3418 1.5844 1.5180 1.3087 1.5253 1.4464 1.3551 1.4918 1.4473 1.2730 1.5026 1.3974 1.3831 1.3419 1.2993 1.2769 1.4759 1.2662 1.3964 1.3712 1.3876 1.2845 1.2756 1.3958 1.2497 1.3182 1.3043 1.3459 1.3585 1.2447 1.2371 1.2159 1.2067 1.3003 1.2858 1.2697 1.3114 1.2683 1.2192 1.2184 1.2071 1.1780 1.2472 1.2340 1.2699 1.1513 1.1774 1.1705 1.1614 1.1334 1.1562 1.1308 1.1292 1.1298 1.1394 1.1298 1.1123 1.0919 1.1029 1.0868 1.0744 1.0531 1.0506 1.0375 1.0326

1.0634 1.0694 1.0751 1.0598 1.0753 1.0726 1.0690 1.0829 1.0991 1.0710 1.0885 1.0919 1.0704 1.1011 1.0963 1.1154 1.1180 1.1229 1.1200 1.1126 1.1347 1.0767 1.1492 1.1545 1.1451 1.1341 1.1709 1.1639 1.1729 1.1653 1.1934 1.1933 1.1838 1.1957 1.2108 1.2171 1.2012 1.1859 1.2649 1.2783 1.2714 1.2695 1.2474 1.2586 1.2721 1.2620 1.3004 1.3338 1.3433 1.3392 1.3530 1.3254 1.3398 1.2512 1.4014 1.4300 1.4293 1.4490 1.4776 1.4551 1.4932 1.5067 1.5549 1.5561 1.5661 1.6085 1.6847 1.6653 1.7093 1.8469 1.9223 1.9915 2.0993 2.1278

0.9017 0.9850 0.8502 1.0092 0.9632 0.9350 0.8710 0.9566 0.9895 1.0088 0.8653 0.9212 1.0235 0.8955 0.9597 0.9935 0.9173 0.9324 1.0328 0.8766 0.9599 0.8899 0.9836 1.0145 1.0293 0.8473 1.0277 0.9293 0.9591 0.9366 1.0076 1.0173 0.8996 1.0376 0.9865 0.9829 0.9416 0.9479 1.0275 1.0399 1.0604 1.0693 0.9584 0.9751 0.9819 0.9192 0.9432 1.0361 1.0405 1.0415 1.0890 0.9679 0.9912 0.8735 1.1214 1.0766 1.0678 1.0867 1.1449 1.0809 1.1464 1.1460 1.1236 1.0694 1.1034 1.1667 1.2056 1.1590 1.2331 1.1763 1.3259 1.3384 1.4010 1.3607

Journal of Chemical and Engineering Data, Vol. 45, No. 4, 2000 567 Table 5. Isobaric Vapor-Liquid Equilibrium Data, Temperature, T, Liquid Phase, xi, and Vapor Phase, yi, Mole Fractions, and Activity Coefficient, γi, for Ethanol (1) + 2-Methyl-2-propanol (2) + Octane (3) at 101.3 kPa T/K

x1

x2

y1

y2

γ1

γ2

γ3

T/K

x1

x2

y1

y2

γ1

γ2

γ3

356.33 356.43 356.53 356.74 356.87 356.16 358.88 355.60 359.04 356.26 355.62 355.36 359.03 357.41 355.98 357.01 355.34 357.13 359.15 356.63 359.03 355.86 355.64 356.35 357.53 357.68 356.04 355.31 358.88 357.24 356.77 356.45 355.91 357.33 356.09 357.65 357.81 356.86 357.53 356.18 357.16 356.15 355.58 356.08 356.63 355.05 356.53 355.53 356.02 356.33 354.97 355.90 356.01 356.01 355.45 355.60 355.66 354.89 354.86 354.60 355.35 355.37 355.33 355.75 354.78 354.76 354.94 354.12 354.67 354.66 355.00 354.66

0.041 0.049 0.058 0.063 0.071 0.071 0.072 0.073 0.079 0.081 0.082 0.082 0.082 0.083 0.085 0.085 0.087 0.088 0.088 0.089 0.090 0.092 0.092 0.093 0.094 0.096 0.096 0.099 0.099 0.103 0.103 0.105 0.106 0.108 0.110 0.112 0.116 0.119 0.130 0.136 0.140 0.146 0.149 0.160 0.163 0.164 0.166 0.171 0.171 0.172 0.184 0.186 0.188 0.190 0.190 0.192 0.201 0.202 0.204 0.213 0.216 0.218 0.222 0.222 0.223 0.228 0.231 0.235 0.246 0.248 0.251 0.253

0.831 0.800 0.766 0.645 0.608 0.716 0.356 0.805 0.311 0.679 0.784 0.866 0.306 0.505 0.716 0.581 0.856 0.524 0.251 0.599 0.254 0.716 0.758 0.637 0.450 0.433 0.679 0.838 0.193 0.482 0.543 0.591 0.674 0.423 0.636 0.355 0.354 0.480 0.256 0.530 0.298 0.499 0.630 0.460 0.197 0.758 0.258 0.582 0.424 0.315 0.729 0.381 0.322 0.321 0.533 0.153 0.209 0.701 0.747 0.088 0.459 0.224 0.223 0.355 0.671 0.717 0.551 0.088 0.613 0.636 0.317 0.687

0.059 0.073 0.090 0.103 0.119 0.101 0.204 0.091 0.241 0.119 0.103 0.093 0.245 0.163 0.117 0.139 0.101 0.165 0.305 0.147 0.299 0.125 0.117 0.141 0.202 0.208 0.138 0.112 0.381 0.195 0.181 0.169 0.150 0.230 0.163 0.275 0.272 0.226 0.372 0.225 0.357 0.251 0.208 0.283 0.478 0.189 0.425 0.245 0.316 0.386 0.213 0.354 0.398 0.402 0.284 0.561 0.511 0.237 0.230 0.657 0.344 0.508 0.514 0.393 0.263 0.255 0.313 0.672 0.300 0.295 0.460 0.284

0.874 0.854 0.830 0.747 0.724 0.773 0.581 0.820 0.539 0.746 0.802 0.860 0.531 0.654 0.761 0.693 0.849 0.660 0.467 0.695 0.469 0.755 0.780 0.714 0.605 0.596 0.731 0.833 0.383 0.622 0.651 0.676 0.720 0.579 0.696 0.518 0.521 0.595 0.408 0.611 0.436 0.580 0.658 0.543 0.308 0.743 0.369 0.612 0.505 0.416 0.712 0.461 0.409 0.405 0.564 0.228 0.286 0.681 0.721 0.132 0.491 0.291 0.287 0.420 0.647 0.691 0.550 0.123 0.591 0.609 0.357 0.656

1.1820 1.2231 1.2712 1.3327 1.3623 1.1831 2.1130 1.0571 2.2780 1.2190 1.0730 0.9787 2.2211 1.5574 1.1533 1.3127 1.0000 1.5107 2.5708 1.3443 2.4878 1.1435 1.0770 1.2497 1.6898 1.7074 1.1923 0.9742 2.8774 1.5157 1.4293 1.3263 1.1877 1.6972 1.2359 1.9284 1.8377 1.5462 2.2666 1.3824 2.0413 1.4280 1.1864 1.4799 2.3994 0.9995 2.0978 1.2213 1.5437 1.8506 1.0049 1.6038 1.7681 1.7752 1.2755 2.4774 2.1555 1.0238 0.9857 2.7243 1.3675 1.9989 1.9923 1.4953 1.0359 0.9808 1.1805 2.5702 1.0767 1.0515 1.5968 0.9910

1.0190 1.0283 1.0400 1.1040 1.1282 1.0527 1.4305 1.0144 1.5083 1.0659 1.0178 0.9993 1.5145 1.2030 1.0429 1.1254 0.9979 1.1814 1.6159 1.1092 1.6117 1.0397 1.0232 1.0849 1.2417 1.2634 1.0549 1.0017 1.7367 1.2039 1.1408 1.1005 1.0503 1.2748 1.0687 1.3403 1.3455 1.1767 1.4743 1.1210 1.3725 1.1341 1.0408 1.1523 1.4911 0.9975 1.3719 1.0512 1.1672 1.2788 0.9975 1.1911 1.2441 1.2359 1.0590 1.4810 1.3608 0.9945 0.9900 1.5434 1.0750 1.3038 1.2956 1.1703 0.9924 0.9914 1.0203 1.4676 0.9965 0.9900 1.1476 0.9874

0.5034 0.4698 0.4379 0.4868 0.4632 0.5735 0.3292 0.7259 0.3141 0.5465 0.7044 0.8861 0.3196 0.4113 0.5999 0.4724 0.8795 0.4224 0.2991 0.4846 0.3071 0.6152 0.6840 0.5177 0.3914 0.3814 0.5705 0.8700 0.2924 0.4124 0.4521 0.4920 0.5840 0.3776 0.5420 0.3576 0.3556 0.4211 0.3304 0.4778 0.3445 0.4638 0.6042 0.4472 0.3208 0.8924 0.3438 0.5769 0.4318 0.3736 0.8863 0.4198 0.3874 0.3867 0.5518 0.3213 0.3414 0.8721 1.0211 0.3135 0.5108 0.3619 0.3610 0.4391 0.8648 1.0273 0.6429 0.3211 0.7926 0.8490 0.4310 1.0243

353.89 354.76 354.75 354.50 354.49 354.58 354.32 353.16 354.47 354.12 354.24 353.93 352.83 352.89 354.04 353.33 353.95 353.85 353.56 353.88 353.63 353.77 353.31 352.10 353.55 352.72 353.11 353.40 353.51 353.48 352.91 352.60 351.72 353.16 353.72 352.94 351.56 352.95 353.17 353.15 351.54 352.16 352.73 353.44 352.33 352.42 351.39 352.71 352.20 353.14 351.18 352.38 351.59 351.47 352.30 351.82 351.72 352.42 351.21 350.66 351.75 351.71 352.35 351.08 351.92 351.13 351.11 351.85 351.31 351.35 350.38 350.76

0.257 0.259 0.270 0.274 0.276 0.282 0.285 0.285 0.295 0.311 0.314 0.314 0.317 0.339 0.343 0.355 0.357 0.359 0.374 0.375 0.385 0.404 0.406 0.409 0.420 0.426 0.434 0.434 0.445 0.445 0.448 0.457 0.457 0.468 0.472 0.476 0.483 0.484 0.490 0.491 0.498 0.504 0.515 0.516 0.534 0.537 0.538 0.545 0.563 0.563 0.568 0.578 0.600 0.628 0.637 0.638 0.659 0.687 0.695 0.696 0.700 0.718 0.722 0.722 0.748 0.764 0.783 0.786 0.818 0.845 0.857 0.911

0.099 0.499 0.319 0.598 0.564 0.303 0.222 0.066 0.431 0.286 0.507 0.212 0.071 0.096 0.424 0.192 0.446 0.363 0.272 0.504 0.355 0.505 0.284 0.084 0.445 0.176 0.280 0.401 0.458 0.455 0.263 0.199 0.070 0.382 0.486 0.320 0.069 0.334 0.403 0.400 0.075 0.174 0.320 0.439 0.238 0.261 0.080 0.337 0.239 0.387 0.075 0.288 0.150 0.152 0.281 0.214 0.208 0.270 0.143 0.061 0.210 0.202 0.244 0.132 0.204 0.137 0.130 0.178 0.129 0.115 0.047 0.045

0.669 0.360 0.472 0.329 0.345 0.494 0.561 0.719 0.421 0.529 0.397 0.583 0.722 0.705 0.458 0.624 0.452 0.501 0.566 0.436 0.521 0.456 0.574 0.735 0.489 0.659 0.588 0.518 0.502 0.502 0.605 0.653 0.753 0.545 0.510 0.582 0.758 0.578 0.549 0.550 0.756 0.685 0.600 0.557 0.652 0.640 0.758 0.606 0.661 0.599 0.767 0.643 0.724 0.730 0.678 0.701 0.712 0.716 0.754 0.795 0.733 0.745 0.749 0.768 0.769 0.784 0.796 0.801 0.822 0.846 0.848 0.891

0.128 0.494 0.346 0.567 0.537 0.325 0.250 0.081 0.423 0.293 0.476 0.228 0.082 0.104 0.396 0.192 0.412 0.341 0.261 0.458 0.325 0.454 0.260 0.080 0.395 0.162 0.250 0.353 0.402 0.401 0.231 0.175 0.063 0.330 0.437 0.273 0.060 0.284 0.346 0.343 0.064 0.146 0.267 0.384 0.195 0.214 0.065 0.279 0.193 0.335 0.059 0.233 0.116 0.116 0.225 0.166 0.159 0.219 0.104 0.044 0.160 0.154 0.197 0.095 0.158 0.100 0.094 0.138 0.096 0.086 0.032 0.032

2.3655 1.2218 1.5366 1.0657 1.1075 1.5494 1.7580 2.3589 1.2687 1.5320 1.1337 1.6814 2.1550 1.9658 1.2061 1.6315 1.1461 1.2699 1.3921 1.0571 1.2399 1.0309 1.3122 1.7517 1.0726 1.4730 1.2699 1.1062 1.0389 1.0394 1.2755 1.3645 1.6295 1.0869 0.9879 1.1517 1.5600 1.1255 1.0461 1.0488 1.5116 1.3209 1.1075 0.9993 1.1787 1.1464 1.4113 1.0578 1.1400 0.9961 1.3651 1.0718 1.2006 1.1603 1.0281 1.0831 1.0696 1.0036 1.0952 1.1774 1.0356 1.0277 1.0003 1.0785 1.0080 1.0384 1.0309 1.0028 1.0108 1.0041 1.0326 1.0049

1.3800 1.0200 1.1183 0.9872 0.9912 1.1127 1.1783 1.3569 1.0231 1.0805 0.9868 1.1437 1.2729 1.2012 0.9900 1.0872 0.9829 1.0012 1.0366 0.9689 0.9852 0.9617 0.9984 1.0812 0.9585 1.0292 0.9820 0.9549 0.9500 0.9536 0.9728 0.9857 1.0491 0.9487 0.9633 0.9457 1.0158 0.9417 0.9411 0.9425 0.9989 0.9558 0.9298 0.9489 0.9271 0.9247 0.9616 0.9270 0.9176 0.9489 0.9339 0.9177 0.9045 0.8940 0.9105 0.8959 0.8892 0.9170 0.8686 0.8661 0.8856 0.8868 0.9152 0.8647 0.8964 0.8695 0.8643 0.8988 0.8756 0.8821 0.8378 0.8651

0.3350 0.6181 0.4553 0.8385 0.7685 0.4517 0.4030 0.3372 0.5900 0.4664 0.7442 0.4247 0.3575 0.3744 0.6634 0.4434 0.7338 0.6094 0.5283 0.9329 0.6415 1.0607 0.5857 0.4190 0.9255 0.5007 0.6214 0.8509 1.0761 1.0642 0.6276 0.5631 0.4526 0.9166 1.3740 0.7858 0.4766 0.8379 1.0838 1.0663 0.4949 0.6013 0.9024 1.4026 0.7651 0.8202 0.5460 1.0816 0.8443 1.4579 0.5794 1.0439 0.7472 0.8261 1.3485 1.0434 1.1231 1.6851 1.0340 0.8090 1.3715 1.4624 1.8357 1.1174 1.7572 1.4019 1.4941 1.9321 1.8258 2.0253 1.5300 2.1113

ternary system are shown in Figures 3 and 4, respectively. The experimental VLE data for the system of ethanol (1)

+ 2-methyl-2-propanol (2) + octane (3) at 101.3 kPa are reported in Table 5 and are shown graphically in Figures

568

Journal of Chemical and Engineering Data, Vol. 45, No. 4, 2000

Figure 4. Isotherms for the ternary system MTBE (1) + ethanol (2) + 2-methyl-2-propanol (3) at 101.3 kPa.

Figure 3. Tie lines for the ternary system MTBE (1) + ethanol (2) + 2-methyl-2-propanol (3) at 101.3 kPa: O, liquid composition; 4, vapor composition. Table 6. Parameters of the NRTL Equation for the Binary Systems system MTBE (1) + ethanol (2) ethanol (1) + 2-methyl-2-propanol (2) MTBE (1) + 2-methyl-2-propanol (2) 2-methyl-2-propanol (1) + octane (2) ethanol (1) + octane (2)

gij - gii

gij - gjj

J‚mol-1

J‚mol-1

Rij

791.988 2501.984 0.47 3108.461 -2282.054 0.47 -793.364 2825.310 0.47 2355.785 2188.091 0.47 5419.983 5029.721 0.47

5 and 6. Each of these systems forms a nonazeotropic mixture. Correlation and Prediction The activity coefficients were correlated with the nonrandom two-liquid (NRTL) equation (eq 9) using the R term as either a fitting parameter or a fixed value. In the case of the systems containing an alcohol with a hydrocarbon or an ether, it was acceptable to correlate using the fixed value of 0.47 as the R term. The parameters in the equation were obtained by using the Marquardt method.10 The sum of the squares of the relative deviations in the activity coefficients was minimized during optimization of the parameters. The NRTL parameters, gij - gii, gij - gjj, and Rij for the five binary systems i-j were determined on the basis of the experimental data. They are shown in Table 6. The calculated results using the NRTL equation are depicted by solid lines in Figures 1 and 2. The average absolute deviations and maximum deviations between the experimental and calculated vapor-phase compositions and tem-

Figure 5. Tie lines for the ternary system ethanol (1) + 2-methyl2-propanol (2) + octane (3) at 101.3 kPa: O, liquid composition; 4, vapor composition.

peratures for the constituent five binary systems are shown in Table 7. The prediction of the ternary VLE was carried out with the NRTL binary parameters in Table 6. For the MTBE (1) + ethanol (2) + 2-methyl-2-propanol (3) system, the average absolute deviations were 0.007 mole fraction in y1, 0.004 mole fraction in y2, and 0.27 K in temperature. Average absolute deviations of 0.006 mole fraction in y1, 0.05 mole fraction in y2, and 0.18 K in temperature were

Table 7. Deviations between Calculated and Experimental Vapor Mole Fractions, ∆yi, and Temperatures, ∆T, of the NRTL Equation for the Binary Systems deviation average

maximum

system

∆yi

∆T/K

∆γ1

∆γ2

∆yi

∆T/K

∆γ1

∆γ2

MTBE (1) + ethanol ethanol (1) + 2-methyl-2-propanol (2) MTBE (1) + 2-methyl-2-propanol (2)b 2-methyl-2-propanol (1) + octane (2)b ethanol (1) + octane (2)c

0.006 0.001 0.003 0.006 0.006

0.13 0.02 0.12 0.12 0.07

0.0130 0.0044 0.0279 0.0122 0.0244

0.0365 0.0022 0.0289 0.1118 0.0512

0.023 0.002 0.007 0.014 0.014

0.46 0.05 0.46 0.35 0.31

0.0483 0.0184 0.1066 0.0467 0.0640

0.0645 0.0044 0.0971 0.2845 0.0885

(2)a

a

Reference 1. b Reference 2. c Reference 4.

Journal of Chemical and Engineering Data, Vol. 45, No. 4, 2000 569

Figure 6. Isotherms for the ternary system ethanol (1) + 2-methyl-2-propanol (2) + octane (3) at 101.3 kPa.

determined for the ethanol (1) + 2-methyl-2-propanol (2) + octane (3) system. Literature Cited (1) Hiaki, T.; Tatsuhana, K.; Tsuji, T.; Hongo, M. Isobaric VaporLiquid Equilibria for 2-Methoxy-2-methylpropane + Ethanol + Octane and Constituent Binary Systems at 101.3 kPa. J. Chem. Eng. Data 1999, 44, 323-327. (2) Hiaki, T.; Tatsuhana, K.; Tsuji, T.; Hongo, M. Vapor-Liquid Equilibria for Binary and Ternary Systems Composed of 2-Methoxy-2-methylpropane, 2-Methyl-2-propanol, Octane at 101.3 kPa. Fluid Phase Equilib. 1999, 156, 161-171.

(3) Hiaki, T.; Yamato, K.; Kojima, K. Vapor-liquid Equilibria of 2,3Dimethylbutane + Methanol or Ethanol at 101.3 kPa. J. Chem. Eng. Data 1992, 37, 203-206. (4) Hiaki, T.; Takahashi, K.; Tsuji, T.; Hongo, M.; Kojima, K. VaporLiquid Equilibria of Ethanol with 2,2,4-Trimethylpentane or Octane at 101.3 kPa. J. Chem. Eng. Data 1994, 39, 720-722. (5) Suska, J.; Holub, R.; Vonka, P.; Pick, J. Liquid-Vapor Equilibriums. XLII. Systems: Ethyl Alcohol-Water-tert-butyl alcohol and Ethyl Alcohol-Water-iso-butyl Alcohol. Collect. Czech. Chem. Commun. 1970, 35, 385-395. (6) Oracz, P. Liquid-Vapor Equilibrium. 2-Methyl-2-propanol-Ethanol System. Int. Data Ser., Sel. Data Mixtures, Ser. A 1989, 290. (7) Fredenslund, A.; Gmehling, J.; Rasmussen, P. Vapor-Liquid Equilibria Using UNIFAC; Elsevier: Amsterdam, 1977. (8) Van Ness, H. C.; Byer, S. M.; Gibbs, R. E. Vapor-liquid equilibrium: Part I. An Appraisal of Data Reduction Methods. AIChE J. 1973, 19, 238-244. (9) Renon, H.; Prausnitz, J. M. Local Compositions in Thermodynamic Excess Functions for Liquid Mixtures. AIChE J. 1968, 14, 135-144. (10) Marquardt, D. W. An Algorithm for Least-squares Estimation of Nonlinear Parameters. J. Soc. Ind. Appl. Math. 1963, 11, 431441. (11) Arce, A.; Martinez-Ageitos, J.; Soto, A. VLE Measurement of Binary Mixtures of Methanol, Ethanol, 2-Methoxy-2-methylpropane, and 2-Methoxy-2-methylbutane at 101.32 kPa. J. Chem. Eng. Data 1996, 41, 718-723. (12) Riddick, J. A.; Bunger, W. B.; Sakano, T. K. Organic Solvents Physical Properties and Methods of Purification, 4th ed.; John Wiley & Sons: New York, 1986. (13) Tsuji, T.; Hiaki, T.; Hongo, M. Vapor Pressure Measurements of Three Ethers: Diisopropyl Ether, Methyl tert-butyl Ether, and tert-Amyl Methyl Ether. Proceedings of the 15th IUPAC Conference on Chemical Thermodynamics, 1998. (14) Boublik, T.; Fried, V.; Hala, E. The Vapor Pressures of Pure Substances, 2nd ed.; Elsevier: Amsterdam, 1984.

Received for review October 26, 1999. Accepted March 20, 2000.

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